Đáp án:
`-\sqrt{2}`
Giải thích các bước giải:
`\qquad (1-\sqrt{3})\sqrt{2+\sqrt{3}}`
`=(1-\sqrt{3}).\sqrt{{4+2\sqrt{3}}/2}`
`=(1-\sqrt{3}).\sqrt{{3+2.\sqrt{3}.1+1^2}/2}`
`=(1-\sqrt{3}).\sqrt{{(\sqrt{3}+1)^2}/2}`
`=(1-\sqrt{3}).|{\sqrt{3}+1}/\sqrt{2}|`
`={(1-\sqrt{3}).(1+\sqrt{3})}/\sqrt{2}`
`={1^2-(\sqrt{3})^2}/\sqrt{2}`
`={-2}/\sqrt{2}=-\sqrt{2}`
Vậy: `(1-\sqrt{3})\sqrt{2+\sqrt{3}}=-\sqrt{2}`